Question

Consider the following linear programming problem:

Maximize	$12X+10Y$
Subject to:	$4X+3Y\le 480$
	$2X+3Y\le 360$
	all variables $\ge 0$

Which of the following points $(X,Y)$ is feasible?

• A. $(10,120)$
• B. $(120,10)$
• C. $(30,100)$
• D. $(60,90)$
• E. None of the above

Answer 1

Answer: (C)

$(30,100)$

Consider point $(10,120)$ , It doesnt satisfy the inequality $2X+3Y\le 360$

Consider point $(120,10)$ , it doesnt satisfy the inequality $4X+3Y\le 480$

Consider point $(30,100)$ , it satisfies all the inequalities . So this point is feasible

Consider point $(60,90)$ , it doesnt satisfies the inequalities $2X+3Y\le 360$ and $4X+3Y\le 480$

Therefore the correct option is $C$